The Program in Mathematics for Young Scientists (PROMYS) (pronounced "promise") is a six-week number theory program currently under the direction of Professor Glenn Stevens at Boston University beginning in early July and ending in mid-August.
The program is open to high school students, although college students and above can return as counselors. Each year, there are roughly 45 first year students and 15 returning students, in addition to undergraduate counselors and junior counselors. The program centers around a daily number theory lecture from Professor Stevens, which is mandatory for everyone. First-year students are typically also involved in an Exploration Lab, an open-ended problem in number theory or a closely related area of math that is accessible to first-year students. Exploration Lab topics have included relationships between Pick's theorem and the Euler characteristic, linear fractional transformations, Linear Diophantine equations, integer partitions and compositions, finite differences, and Chebyshev polynomials.
Returning students, some of whom are attending the program for the third or even fourth time, typically take advanced courses sponsored by the Clay Mathematics Institute participate in a Research Lab, although all courses and labs are open to all students. Advanced courses are taught by professors at Boston University and other schools, including Brandeis University and Syracuse University. In addition, there are several minicourses and guest lectures on a wide variety of mathematical topics.
Research topics have included Ducci sequences (also known as the n-numbers game), dragon curves, arithmetrees, and tropical algebraic geometry. In 2008 the advanced courses featured Galois theory, representation theory of finite groups, and geometry. Through dealing a usually intuitive subject with mathematical rigor, the geometry course exposes its students to many areas of mathematics, including set theory, algebra, and non-Euclidean geometry. 2009 featured advanced courses in linear algebra, combinatorics, and geometry. The 2010 advanced courses were in abstract algebra, modular forms, and geometry & symmetry.
Students are required to do problem sets every weekday and one extra long problem set on the weekend. Every Friday night, the counselors organize "an event so fun that it is necessary and sufficient," hence the name "mandatory fun." These events include a picnic, casino night, a talent show, animation night, a "dance," and an ice cream social. Also during the weekends, students usually participate in games of Egyptian Rat Screw, Illuminati, or Mafia lasting entire nights.
The counselors also hold informal seminars of various topics, such as the p-adic number system. During some nights a guest lecture is organized where mathematicians and people working in math-related subjects such as Wolfram Group lecture on what they find interesting and worth sharing.
The predecessor to PROMYS was the Ross program, of which Professor Stevens and many of the advanced course instructors are graduates.
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